Tree Graphs and Orthogonal Spanning Tree Decompositions

Tree Graphs and Orthogonal Spanning Tree Decompositions

Book Details:

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Global

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Category

Year:

2016

Publisher:

Portland State University

Pages:

106 pages

Language:

english

Since:

11/01/2017

Size:

1.05 MB

License:

CC-BY-SA

Content:

Given a graph G, we construct T (G), called the tree graph of G. The vertices of T (G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs.

While many papers about tree graphs have been published over the last half century, there is still much that remains to be considered, including many classic graph parameters, such as the clique number and independence number. Other standard graph theoretic concepts such as planarity, decomposition, and regularity, as well as more algebraic topics, like automorphism groups, vertex-transitivity, and integrality, are likewise ripe for exploration.